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\n  \n 2022\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n An end-to-end data-driven optimization framework for constrained trajectories.\n \n \n \n\n\n \n Dewez, F.; Guedj, B.; Talpaert, A.; and Vandewalle, V.\n\n\n \n\n\n\n Data-Centric Engineering, 3: e6. 2022.\n \n\n\n\n
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@article{dewez_guedj_talpaert_vandewalle_2022,\n\ttitle={An end-to-end data-driven optimization framework for constrained trajectories},\n\tvolume={3}, DOI={10.1017/dce.2022.6},\n\tjournal={Data-Centric Engineering},\n\tpublisher={Cambridge University Press},\n\tauthor={Dewez, Florent and Guedj, Benjamin and Talpaert, Arthur and Vandewalle, Vincent},\n\tyear={2022},\n\tpages={e6}\n}\n\n
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\n \n\n \n \n \n \n \n \n Time-asymptotic propagation of approximate solutions of Schrödinger equations with both potential and initial condition in Fourier-frequency bands .\n \n \n \n \n\n\n \n Dewez, F.\n\n\n \n\n\n\n 2021.\n Submitted\n\n\n\n
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@unpublished{dewez021,\n\ttitle = {Time-asymptotic propagation of approximate solutions of Schrödinger equations with both potential and initial condition in Fourier-frequency bands },\n\tauthor = {Dewez, Florent},\n\tyear = {2021},\n\tnote = {Submitted},\n\turl = {https://arxiv.org/abs/1707.09756}\n}\n\n
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\n \n\n \n \n \n \n \n From industry-wide parameters to aircraft-centric on-flight inference: Improving aeronautics performance prediction with machine learning.\n \n \n \n\n\n \n Dewez, F.; Guedj, B.; and Vandewalle, V.\n\n\n \n\n\n\n Data-Centric Engineering, 1: e11. 2020.\n \n\n\n\n
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@article{dewez_guedj_vandewalle_2020,\n\ttitle = {From industry-wide parameters to aircraft-centric on-flight inference: Improving aeronautics performance prediction with machine learning},\n\tvolume = {1}, DOI={10.1017/dce.2020.12},\n\tjournal = {Data-Centric Engineering},\n\tpublisher = {Cambridge University Press},\n\tauthor = {Dewez, Florent and Guedj, Benjamin and Vandewalle, Vincent},\n\tyear = {2020},\n\tpages = {e11}\n}\n\n
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\n \n\n \n \n \n \n \n \n Stability of propagation features under time-asymptotic approximations for a class of dispersive equations.\n \n \n \n \n\n\n \n Dewez, F.\n\n\n \n\n\n\n Journal of Mathematical Analysis and Applications, 491(1): 124292. 2020.\n \n\n\n\n
\n\n\n\n \n \n \"StabilityPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 2 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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@article{DEWEZ2020124292,\n\ttitle = "Stability of propagation features under time-asymptotic approximations for a class of dispersive equations",\n\tjournal = "Journal of Mathematical Analysis and Applications",\n\tvolume = "491",\n\tnumber = "1",\n\tpages = "124292",\n\tyear = "2020",\n\tissn = "0022-247X",\n\tdoi = "https://doi.org/10.1016/j.jmaa.2020.124292",\n\turl = "http://www.sciencedirect.com/science/article/pii/S0022247X20304546",\n\tauthor = "Florent Dewez",\n\tkeywords = "Wave packet, Dispersive equation, Oscillatory integral, Stationary phase method, Frequency band",\n\tabstract = "We consider solutions of dispersive equations on the line defined by Fourier multipliers with initial data having compactly supported Fourier transforms. In this paper, a refinement of an existing method permitting to expand time-asymptotically the solution formulas is proposed. Here the first term of the expansion is supported in a space-time cone whose origin depends explicitly on the initial datum. As an important consequence of our refined method, the first term inherits the mean position of the solution together with a constant variance error and a shifted time-decay rate is obtained. Hence this refinement, which takes into account both spatial and frequency information of the initial datum, makes stable some propagation features under time-asymptotic approximations and permits a better description of the time-asymptotic behaviour of the solutions. The results are achieved firstly by making apparent the cone origin in the solution formula, secondly by applying precisely an adapted version of the stationary phase method with a new error bound, and finally by minimising the error bound with respect to the cone origin."\n}\n\n
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\n We consider solutions of dispersive equations on the line defined by Fourier multipliers with initial data having compactly supported Fourier transforms. In this paper, a refinement of an existing method permitting to expand time-asymptotically the solution formulas is proposed. Here the first term of the expansion is supported in a space-time cone whose origin depends explicitly on the initial datum. As an important consequence of our refined method, the first term inherits the mean position of the solution together with a constant variance error and a shifted time-decay rate is obtained. Hence this refinement, which takes into account both spatial and frequency information of the initial datum, makes stable some propagation features under time-asymptotic approximations and permits a better description of the time-asymptotic behaviour of the solutions. The results are achieved firstly by making apparent the cone origin in the solution formula, secondly by applying precisely an adapted version of the stationary phase method with a new error bound, and finally by minimising the error bound with respect to the cone origin.\n
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\n \n\n \n \n \n \n \n \n Decrypting the Hill Cipher via a Restricted Search over the Text-Space.\n \n \n \n \n\n\n \n Dewez, F.; and Montmirail, V.\n\n\n \n\n\n\n In Schmeh, K.; and Antal, E., editor(s), Proceedings of the 2nd International Conference on Historical Cryptology, HistoCrypt 2019, Mons, Belgium, June 23-26, 2019, volume 158, of Linköping Electronic Conference Proceedings, pages 158:002, 2019. Linköping University Electronic Press\n \n\n\n\n
\n\n\n\n \n \n \"DecryptingPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n  \n \n 2 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@inproceedings{DBLP:conf/histocrypt/DewezM19,\n\tauthor    = {Florent Dewez and\n\t\t\t\tValentin Montmirail},\n\teditor    = {Klaus Schmeh and\n\t\t\t\tEugen Antal},\n\ttitle     = {Decrypting the Hill Cipher via a Restricted Search over the Text-Space},\n\tbooktitle = {Proceedings of the 2nd International Conference on Historical Cryptology,\n\t\t\t\tHistoCrypt 2019, Mons, Belgium, June 23-26, 2019},\n\tseries    = {Link{\\"{o}}ping Electronic Conference Proceedings},\n\tvolume    = {158},\n\tpages     = {158:002},\n\tpublisher = {Link{\\"{o}}ping University Electronic Press},\n\tyear      = {2019},\n\turl       = {http://www.ep.liu.se/ecp/article.asp?issue=158\\&article=002\\&volume=},\n\ttimestamp = {Thu, 10 Oct 2019 13:06:30 +0200},\n\tbiburl    = {https://dblp.org/rec/conf/histocrypt/DewezM19.bib},\n\tbibsource = {dblp computer science bibliography, https://dblp.org}\n}\n\n
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\n  \n 2018\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Estimates of oscillatory integrals with stationary phase and singular amplitude: Applications to propagation features for dispersive equations.\n \n \n \n \n\n\n \n Dewez, F.\n\n\n \n\n\n\n Mathematische Nachrichten, 291(5-6): 793-826. 2018.\n \n\n\n\n
\n\n\n\n \n \n \"EstimatesPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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@article{doi:10.1002/mana.201600218,\n\tauthor = {Dewez, Florent},\n\ttitle = {Estimates of oscillatory integrals with stationary phase and singular amplitude: Applications to propagation features for dispersive equations},\n\tjournal = {Mathematische Nachrichten},\n\tvolume = {291},\n\tnumber = {5-6},\n\tpages = {793-826},\n\tkeywords = {Oscillatory integral, van der Corput Lemma, dispersive equation, frequency band, singular frequency, space-time cone, (optimal) time-decay rate, Primary: 35B40; Secondary: 35B30, 35Q40, 35Q41, 35S10},\n\tdoi = {10.1002/mana.201600218},\n\turl = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mana.201600218},\n\teprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.201600218},\n\tabstract = {Abstract In this paper, we study time-asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of phases which may have a stationary point of real order and amplitudes allowed to have an integrable singular point. The resulting estimates provide optimal decay rates which show explicitly the influence of these two particular points. Then we apply these abstract results to solution formulas of a class of dispersive equations on the line defined by Fourier multipliers. Under the hypothesis that the Fourier transform of the initial data has a compact support or an integrable singular point, we derive uniform estimates of the solutions in space-time cones, describing their motions when the time tends to infinity. The method permits also to show that symbols having a restricted growth at infinity may influence the dispersion of the solutions: we prove the existence of a cone, depending only on the symbol, in which the solution is time-asymptotically localized. This corresponds to an asymptotic version of the notion of causality for initial data without compact support.},\n\tyear = {2018}\n}\n\n
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\n Abstract In this paper, we study time-asymptotic propagation phenomena for a class of dispersive equations on the line by exploiting precise estimates of oscillatory integrals. We propose first an extension of the van der Corput Lemma to the case of phases which may have a stationary point of real order and amplitudes allowed to have an integrable singular point. The resulting estimates provide optimal decay rates which show explicitly the influence of these two particular points. Then we apply these abstract results to solution formulas of a class of dispersive equations on the line defined by Fourier multipliers. Under the hypothesis that the Fourier transform of the initial data has a compact support or an integrable singular point, we derive uniform estimates of the solutions in space-time cones, describing their motions when the time tends to infinity. The method permits also to show that symbols having a restricted growth at infinity may influence the dispersion of the solutions: we prove the existence of a cone, depending only on the symbol, in which the solution is time-asymptotically localized. This corresponds to an asymptotic version of the notion of causality for initial data without compact support.\n
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\n \n\n \n \n \n \n \n \n Le jeu du Lights Out: Une approche visuelle des Mathématiques au travers d'un atelier.\n \n \n \n \n\n\n \n Defourneau, T.; Dewez, F.; and Montmirail, V.\n\n\n \n\n\n\n MathémaTICE, 54. March 2017.\n Online version in French.\n\n\n\n
\n\n\n\n \n \n \"LePaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@article{tdfdvm2017,\n\tauthor = {Defourneau, Thibault and Dewez, Florent and Montmirail, Valentin},\n\ttitle = {Le jeu du Lights Out: Une approche visuelle des Mathématiques au travers d'un atelier},\n\tjournal = {MathémaTICE},\n\tvolume = {54},\n\turl = {http://revue.sesamath.net/spip.php?article950},\n\tyear = {2017},\n\tmonth = {March},\n\tnote = {Online version in French.}\n}\n\n
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\n \n\n \n \n \n \n \n \n Lossless error estimates for the stationary phase method with applications to propagation features for the Schrödinger equation.\n \n \n \n \n\n\n \n Ali Mehmeti, F.; and Dewez, F.\n\n\n \n\n\n\n Mathematical Methods in the Applied Sciences, 40(3): 626-662. 2017.\n \n\n\n\n
\n\n\n\n \n \n \"LosslessPaper\n  \n \n\n \n \n doi\n  \n \n\n \n link\n  \n \n\n bibtex\n \n\n \n  \n \n abstract \n \n\n \n  \n \n 1 download\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n \n\n\n\n
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@article{doi:10.1002/mma.3998,\n\tauthor = {Ali Mehmeti, Felix and Dewez, Florent},\n\ttitle = {Lossless error estimates for the stationary phase method with applications to propagation features for the Schrödinger equation},\n\tjournal = {Mathematical Methods in the Applied Sciences},\n\tvolume = {40},\n\tnumber = {3},\n\tpages = {626-662},\n\tkeywords = {asymptotic expansion, stationary phase method, error estimate, Schrödinger equation, L∞-time decay, singular frequency, space-time cone},\n\tdoi = {10.1002/mma.3998},\n\turl = {https://onlinelibrary.wiley.com/doi/abs/10.1002/mma.3998},\n\teprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.3998},\n\tabstract = {We consider a version of the stationary phase method in one dimension of A. Erdélyi, allowing the phase to have stationary points of non-integer order and the amplitude to have integrable singularities. After having completed the original proof and improved the error estimate in the case of regular amplitude, we consider a modification of the method by replacing the smooth cut-off function employed in the source by a characteristic function, leading to more precise remainder estimates. We exploit this refinement to study the time-asymptotic behaviour of the solution of the free Schrödinger equation on the line, where the Fourier transform of the initial data is compactly supported and has a singularity. We obtain asymptotic expansions with respect to time in certain space-time cones as well as uniform and optimal estimates in curved regions, which are asymptotically larger than any space-time cone. These results show the influence of the frequency band and of the singularity on the propagation and on the decay of the wave packets. Copyright © 2016 John Wiley \\& Sons, Ltd.},\n\tyear = {2017}\n}\n\n
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\n We consider a version of the stationary phase method in one dimension of A. Erdélyi, allowing the phase to have stationary points of non-integer order and the amplitude to have integrable singularities. After having completed the original proof and improved the error estimate in the case of regular amplitude, we consider a modification of the method by replacing the smooth cut-off function employed in the source by a characteristic function, leading to more precise remainder estimates. We exploit this refinement to study the time-asymptotic behaviour of the solution of the free Schrödinger equation on the line, where the Fourier transform of the initial data is compactly supported and has a singularity. We obtain asymptotic expansions with respect to time in certain space-time cones as well as uniform and optimal estimates in curved regions, which are asymptotically larger than any space-time cone. These results show the influence of the frequency band and of the singularity on the propagation and on the decay of the wave packets. Copyright © 2016 John Wiley & Sons, Ltd.\n
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\n  \n 2016\n \n \n (1)\n \n \n
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\n \n\n \n \n \n \n \n \n Estimations sans pertes pour des méthodes asymptotiques et notion de propagation pour des équations dispersives.\n \n \n \n \n\n\n \n Dewez, F.\n\n\n \n\n\n\n Ph.D. Thesis, 2016.\n 2016LIL10095\n\n\n\n
\n\n\n\n \n \n \"EstimationsPaper\n  \n \n\n \n\n \n link\n  \n \n\n bibtex\n \n\n \n\n \n  \n \n 3 downloads\n \n \n\n \n \n \n \n \n \n \n\n  \n \n \n\n\n\n
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@phdthesis{dewez2016,\n\turl = "http://www.theses.fr/2016LIL10095",\n\ttitle = "Estimations sans pertes pour des méthodes asymptotiques et notion de propagation pour des équations dispersives",\n\tauthor = "Dewez, Florent",\n\tyear = "2016",\n\tnote = "Thèse de doctorat dirigée par Creusé, Emmanuel et Ali Mehmeti, Felix Mathématiques appliquées Lille 1 2016",\n\tnote = "2016LIL10095",\n\turl = "http://www.theses.fr/2016LIL10095/document",\n}\n\n
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\n \n\n \n \n \n \n \n \n Asymptotic estimates of oscillatory integrals with general phase and singular amplitude: Applications to dispersive equations.\n \n \n \n \n\n\n \n Dewez, F.\n\n\n \n\n\n\n 2015.\n The results of this paper have been completed and published in 'Estimates of oscillatory integrals with stationary phase and singular amplitude: Applications to propagation features for dispersive equations'\n\n\n\n
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@unpublished{dewez2015,\n\tauthor = {Dewez, Florent},\n\ttitle = {Asymptotic estimates of oscillatory integrals with general phase and singular amplitude: Applications to dispersive equations},\n\turl = {https://arxiv.org/pdf/1507.00883.pdf},\n\tyear = {2015},\n\tnote = {The results of this paper have been completed and published in 'Estimates of oscillatory integrals with stationary phase and singular amplitude: Applications to propagation features for dispersive equations'}\n}\n\n
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\n \n\n \n \n \n \n \n \n Explicit error estimates for the stationary phase method II: The influence of amplitude singularities.\n \n \n \n \n\n\n \n Ali Mehmeti, F.; and Dewez, F.\n\n\n \n\n\n\n 2014.\n The results of this paper have been published in the merged paper 'Lossless error estimates for the stationary phase method with applications to propagation features for the Schrödinger equation'\n\n\n\n
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@unpublished{dewez2014ii,\n\tauthor = {Ali Mehmeti, Felix and Dewez, Florent},\n\ttitle = {Explicit error estimates for the stationary phase method II: The influence of amplitude singularities},\n\turl = {https://arxiv.org/pdf/1412.5792.pdf},\n\tyear = {2014},\n\tnote = {The results of this paper have been published in the merged paper 'Lossless error estimates for the stationary phase method with applications to propagation features for the Schrödinger equation'}\n}\n\n
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\n \n\n \n \n \n \n \n \n Explicit error estimates for the stationary phase method I: The influence of amplitude singularities.\n \n \n \n \n\n\n \n Ali Mehmeti, F.; and Dewez, F.\n\n\n \n\n\n\n 2014.\n The results of this paper have been published in the merged paper 'Lossless error estimates for the stationary phase method with applications to propagation features for the Schrödinger equation'\n\n\n\n
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@unpublished{dewez2014i,\n\tauthor = {Ali Mehmeti, Felix and Dewez, Florent},\n\ttitle = {Explicit error estimates for the stationary phase method I: The influence of amplitude singularities},\n\turl = {https://arxiv.org/pdf/1412.5789.pdf},\n\tyear = {2014},\n\tnote = {The results of this paper have been published in the merged paper 'Lossless error estimates for the stationary phase method with applications to propagation features for the Schrödinger equation'}\n}
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